Solve 6/8+4/15-3/12+3/9-frac{2}{20}

$$\frac{ 6 }{ 8 } + \frac{ 4 }{ 15 } - \frac{ 3 }{ 12 } + \frac{ 3 }{ 9 } - \frac{ 2 }{ 20 }$$

Evaluate

$$1$$

Solution Steps

Reduce the fraction \frac{6}{8} to lowest terms by extracting and canceling out 2.

$$\frac{3}{4}+\frac{4}{15}-\frac{3}{12}+\frac{3}{9}-\frac{2}{20}$$

Least common multiple of 4 and 15 is 60. Convert \frac{3}{4} and \frac{4}{15} to fractions with denominator 60.

$$\frac{45}{60}+\frac{16}{60}-\frac{3}{12}+\frac{3}{9}-\frac{2}{20}$$

Since \frac{45}{60} and \frac{16}{60} have the same denominator, add them by adding their numerators.

$$\frac{45+16}{60}-\frac{3}{12}+\frac{3}{9}-\frac{2}{20}$$

Add 45 and 16 to get 61.

$$\frac{61}{60}-\frac{3}{12}+\frac{3}{9}-\frac{2}{20}$$

Reduce the fraction \frac{3}{12} to lowest terms by extracting and canceling out 3.

$$\frac{61}{60}-\frac{1}{4}+\frac{3}{9}-\frac{2}{20}$$

Least common multiple of 60 and 4 is 60. Convert \frac{61}{60} and \frac{1}{4} to fractions with denominator 60.

$$\frac{61}{60}-\frac{15}{60}+\frac{3}{9}-\frac{2}{20}$$

Since \frac{61}{60} and \frac{15}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{61-15}{60}+\frac{3}{9}-\frac{2}{20}$$

Subtract 15 from 61 to get 46.

$$\frac{46}{60}+\frac{3}{9}-\frac{2}{20}$$

Reduce the fraction \frac{46}{60} to lowest terms by extracting and canceling out 2.

$$\frac{23}{30}+\frac{3}{9}-\frac{2}{20}$$

Reduce the fraction \frac{3}{9} to lowest terms by extracting and canceling out 3.

$$\frac{23}{30}+\frac{1}{3}-\frac{2}{20}$$

Least common multiple of 30 and 3 is 30. Convert \frac{23}{30} and \frac{1}{3} to fractions with denominator 30.

$$\frac{23}{30}+\frac{10}{30}-\frac{2}{20}$$

Since \frac{23}{30} and \frac{10}{30} have the same denominator, add them by adding their numerators.

$$\frac{23+10}{30}-\frac{2}{20}$$

Add 23 and 10 to get 33.

$$\frac{33}{30}-\frac{2}{20}$$

Reduce the fraction \frac{33}{30} to lowest terms by extracting and canceling out 3.

$$\frac{11}{10}-\frac{2}{20}$$

Reduce the fraction \frac{2}{20} to lowest terms by extracting and canceling out 2.

$$\frac{11}{10}-\frac{1}{10}$$

Since \frac{11}{10} and \frac{1}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{11-1}{10}$$

Subtract 1 from 11 to get 10.

$$\frac{10}{10}$$

Divide 10 by 10 to get 1.

$$1$$

Factor

$$1$$